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Topological Methods in Nonlinear Analysis

Characterization of regularity sets for families of sequences of matrices
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Characterization of regularity sets for families of sequences of matrices

Authors

  • Luis Barreira https://orcid.org/0000-0003-4655-5792
  • Claudià Valls https://orcid.org/0000-0001-8279-1229

Keywords

Lyapunov regularity, sequences of matrices

Abstract

We show that the regularity set of any family of sequences of matrices is an $F_{\sigma\delta}$-set. Moreover, for any $F_{\sigma\delta}$-set containing zero, we construct a family of sequences of matrices having this regularity set.

References

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L. Barreira and C. Valls, Lyapunov regularity and triangularization for unbounded sequences, Electron. J. Qual. Theory Differ. Equ. 2019, Paper No. 53, 31 pp.

L. Barreira and C. Valls, Regularity and stability sets for families of sequences of matrices, J. Dynam. Differential Equations 32 (2020), 1603–1630.

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Ya. Pesin, Lectures on Partial Hyperbolicity and Stable Ergodicity, Zurich Lectures in Advanced Mathematics, European Mathematical Society, Zürich, 2004.

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Published

2021-06-02

How to Cite

1.
BARREIRA, Luis and VALLS, Claudià. Characterization of regularity sets for families of sequences of matrices. Topological Methods in Nonlinear Analysis. Online. 2 June 2021. Vol. 57, no. 2, pp. 675 - 693. [Accessed 7 November 2025].
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